"A visit by your Holiness to visit Sri Lanka would be a momentous occasion to all Sri Lankans, and I earnestly hope I will soon have the honour of welcoming Your Holiness to our shores," Rajapaksa's invitation said.
The invitation comes days after Pope Francis expressed idea to make Sri Lanka a part of his proposed Asian tour.
Sri Lanka has seen two Papal visits -in 1970 Pope Paul VI visited while in 1995 Pope John Paul II visited the island.
Sri Lanka is a Buddhist majority island with 74 per cent of the 20 million people following Buddhist faith.